Recently, square-root topological phase is discovered as a new class
of matter [1]}, whose topological properties are inherited
from its squared parent model through a process analogous to the transition
from Klein-Gordon [2]}, [3]} to Dirac equations [4]}
in relativistic quantum mechanics. In-gap topological edge modes are
found in tight-binding models of square-root topological insulators,
superconductors and semimetals [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
Moreover, general rules of constructing \(2^{n}\) th-root topological
phases [10]}, [16]}, [17]} and symmetry-based classifications
of these intriguing states [14]} are proposed. Experimental
evidence of square-root topological phases has also been reported
in photonic [6]}, electric [7]} and acoustic [8]}
systems.
